Re: Why does butter, when warmed in a microwave oven, melt from the inside out?

Microwave ovens heat food by oscillating water molecules.  
The magnetron of the oven produces microwaves that are absorbed by the water within the food.  
The oscillations of the water transfer heat to the food.  
How well that heat is transferred is a function of the amount of microwave absorbed by the water and the food's ability to accept the heat.

How far microwaves are able to penetrate into the food will also depend on the thickness of portions and on the composition and moisture content of the food.   
Butter tends to absorb the energy in its center more intensely perhaps do to a difference in moisture content, as you suggest.
But more likely an effect produced by the absorption of heat in the bulk.  Surface butter losses some of the heat to the surrounding air, while the butter at the center has energy coming in 
from all sides and only more butter to transfer heat to. Whether the heat is absorbed inside-out or outside-in is a completed function of the material.

Care should be taken that frozen food has been completely thawed. Water absorbs microwaves far more easily than ice does.
Incomplete thawing will result in uneven cooking and the potential survival of undesirable microorganisms in those parts of the food 
which have been insufficiently heated.  This is especially a problem in pork and ground beef.

In many foods, there is a very significant difference in absorption with temperature and ice content.  
Frozen meat tends to heat outside in.  Sometimes this is associated with the level of freezing in the food.  Frozen meat can be "colder" in the center than in the surface edges.  Some technical manuals suggest uniform heating can be achieved in meat by deep freezing the edges. 

Food cooked in a microwave oven does not heat uniformly and unwanted microorganisms may survive in portions of poorly heated food unless something is done to help distribute the heat more uniformly.  
Manufacturers use stirrer fans and turntables and recommend standing times to help alleviate the problem of uneven heating.   Many microwaveable meal packs carry the instruction to stir the food part way through the cooking process. Items such as lasagna that can't be stirred should be allowed standing time to allow the whole product to reach a uniform temperature.

When heating large quantities of food it is more effective to divide it into smaller portions for reheating than it is to heat a large amount for longer time.  
Breaking the food up into smaller chunks reduces the volume to surface disparities so the smaller centers heat more uniformly and quickly.

A positive feature of microwave ovens with regard to food safety is that food can be taken from the freezer, thawed quickly, 
cooked and served without it spending long periods of time in the danger temperature zone between 4°C and 60°C, which provides favorable conditions for the growth of dangerous microorganisms.


Sincerely,
Tom Cull 
Microwave Chef